The Isomorphic Version of Brualdi’s and Sanderson’s Nestedness
AbstractThe discrepancy BR for an m × n 0, 1-matrix from Brualdi and Sanderson in 1998 is defined as the minimum number of 1 s that need to be shifted in each row to the left to achieve its Ferrers matrix, i.e., each row consists of consecutive 1 s followed by consecutive 0 s. For ecological bipartite networks, BR describes a nested set of relationships. Since two different labelled networks can be isomorphic, but possess different discrepancies due to different adjacency matrices, we define a metric determining the minimum discrepancy in an isomorphic class. We give a reduction to k ≤ n minimum weighted perfect matching problems. We show on 289 ecological matrices (given as a benchmark by Atmar and Patterson in 1995) that classical discrepancy can underestimate the nestedness by up to 30%. View Full-Text
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Berger, A.; Schreck, B. The Isomorphic Version of Brualdi’s and Sanderson’s Nestedness. Algorithms 2017, 10, 74.
Berger A, Schreck B. The Isomorphic Version of Brualdi’s and Sanderson’s Nestedness. Algorithms. 2017; 10(3):74.Chicago/Turabian Style
Berger, Annabell; Schreck, Berit. 2017. "The Isomorphic Version of Brualdi’s and Sanderson’s Nestedness." Algorithms 10, no. 3: 74.